##
**Modeling flexible generator operating regions via chance-constrained stochastic unit commitment.**
*(English)*
Zbl 07304212

Summary: We introduce a novel chance-constrained stochastic unit commitment model to address uncertainty in renewables’ production in operations of power systems. For most thermal generators, underlying technical constraints that are universally treated as “hard” by deterministic unit commitment models are in fact based on engineering judgments, such that system operators can periodically request operation outside these limits in non-nominal situations, e.g., to ensure reliability. We incorporate this practical consideration into a chance-constrained stochastic unit commitment model, specifically by infrequently allowing minor deviations from the minimum and maximum thermal generator power output levels. We demonstrate that an extensive form of our model is computationally tractable for medium-sized power systems given modest numbers of scenarios for renewables’ production. We show that the model is able to potentially save significant annual production costs by allowing infrequent and controlled violation of the traditionally hard bounds imposed on thermal generator production limits. Finally, we conduct a sensitivity analysis of optimal solutions to our model under two restricted regimes and observe similar qualitative results.

### MSC:

90Bxx | Operations research and management science |

### Keywords:

stochastic optimization; unit commitment; power systems operations; chance constraints; emergency operations
PDF
BibTeX
XML
Cite

\textit{B. Singh} et al., Comput. Manag. Sci. 17, No. 2, 309--326 (2020; Zbl 07304212)

Full Text:
DOI

### References:

[1] | Anjos MF, Conejo AJ (2017) Unit commitment in electric energy systems, vol. 1, pp. 220-310. Now Publishers, Inc |

[2] | Barrows, C.; Bloom, A.; Ehlen, A.; Jorgenson, J.; Krishnamurthy, D.; Lau, J.; McBennett, B.; O’Connell, M.; Preston, E.; Staid, AS; Watson, JP, The IEEE reliability test system: a proposed 2019 update, IEEE Trans Power Syst, 35, 1, 119-127 (2020) |

[3] | Birge, JR; Louveaux, F., Introduction to stochastic programming (2011), Berlin: Springer Science and Business Media, Berlin · Zbl 1223.90001 |

[4] | Blumsack S (2018) Basic economics of power generation, transmission and distribution. https://www.e-education.psu.edu/eme801/node/530. [Online; accessed September 10, 2018] |

[5] | Borghetti, A.; Frangioni, A.; Lacalandra, F.; Nucci, CA, Lagrangian heuristics based on disaggregated bundle methods for hydrothermal unit commitment, IEEE Trans Power Syst, 18, 1, 313-323 (2003) |

[6] | Cornelius A (2014) Assessing the impact of flexible ramp capability products in the Midcontinent ISO. Master’s thesis |

[7] | Dahal, KP; Chakpitak, N., Generator maintenance scheduling in power systems using metaheuristic-based hybrid approaches, Electr Power Syst Res, 77, 7, 771-779 (2007) |

[8] | Damcı-Kurt, P.; Küçükyavuz, S.; Rajan, D.; Atamtürk, A., A polyhedral study of production ramping, Math Program, 158, 1-2, 175-205 (2016) · Zbl 1346.90627 |

[9] | Gurobi Optimization (2018) Gurobi optimizer reference manual. http://www.gurobi.com. [Online; accessed 19-January-2019] |

[10] | Hart WE, Laird CD, Watson JP, Woodruff DL, Hackebeil GA, Nicholson BL, Siirola JD (2017) Pyomo-optimization modeling in Python, vol. 67, second edn. Springer Science and Business Media, Berlin · Zbl 1370.90003 |

[11] | Kargarian, A.; Fu, Y.; Wu, H., Chance-constrained system of systems based operation of power systems, IEEE Trans Power Syst, 31, 5, 3404-3413 (2016) |

[12] | Kazarlis, SA; Bakirtzis, A.; Petridis, V., A genetic algorithm solution to the unit commitment problem, IEEE Trans Power Syst, 11, 1, 83-92 (1996) |

[13] | Knudsen J, Bendtsen J, Andersen P, Madsen K, Sterregaard C, Rossiter A (2017) Fuel optimization in multiple diesel driven generator power plants. In: 2017 IEEE Conference on Control Technology and Applications (CCTA), pp. 493-498. IEEE |

[14] | Knueven B, Ostrowski J, Watson JP (2018) On mixed integer programming formulations for the unit commitment problem. http://www.optimization-online.org/DB_FILE/2018/11/6930.pdf. [Online; accessed 20-January-2019] |

[15] | Knueven, B.; Ostrowski, J.; Watson, J., A novel matching formulation for startup costs in unit commitment, Math Prog Comp, 12, 225-248 (2020) · Zbl 07241047 |

[16] | Kraemer B (2013) Understanding generator set ratings for maximum performance and reliability. https://www.mtuonsiteenergy.com/fileadmin/fm-dam/mtu_onsite_energy/6_press/technical-articles/en/3156391_OE_TechnicalArticle_Reliability_2010.pdf. [Online; accessed 22-January-2019] |

[17] | MISO (2018) Business practices manual energy and operating reserve markets. https://www.misoenergy.org/legal/business-practice-manuals/. [Online; accessed January 15, 2019] |

[18] | Morales-España, G.; Latorre, JM; Ramos, A., Tight and compact MILP formulation for the thermal unit commitment problem, IEEE Trans Power Syst, 28, 4, 4897-4908 (2013) |

[19] | O’Neill RP (2007) It’s getting better all the time (with mixed integer programming). HEPG Forty-Ninth Plenary Session |

[20] | O’Neill RP (2017) Computational issues in ISO market models. Workshop on Energy Systems and Optimization |

[21] | Ostrowski, J.; Anjos, MF; Vannelli, A., Modified orbital branching for structured symmetry with an application to unit commitment, Math Program, 150, 1, 99-129 (2015) · Zbl 1309.90059 |

[22] | Ott AL (2010) Evolution of computing requirements in the PJM market: past and future. In: Power and Energy Society General Meeting, 2010 IEEE, pp. 1-4. IEEE |

[23] | Ozturk, UA; Mazumdar, M.; Norman, BA, A solution to the stochastic unit commitment problem using chance constrained programming, IEEE Trans Power Syst, 19, 3, 1589-1598 (2004) |

[24] | Padhy, NP, Unit commitment-a bibliographical survey, IEEE Trans Power Syst, 19, 2, 1196-1205 (2004) |

[25] | Power Water (2017) System control operational document—policy. https://www.powerwater.com.au/__data/assets/pdf_file/0013/142321/Secure_System_Guidelines_Draft_3.pdf. [Online; accessed September 9, 2018] |

[26] | Pozo, D.; Contreras, J., A chance-constrained unit commitment with an \(n-k\) security criterion and significant wind generation, IEEE Trans Power Syst, 28, 3, 2842-2851 (2013) |

[27] | Prékopa, A., Boole-bonferroni inequalities and linear programming, Oper Res, 36, 1, 145-162 (1988) · Zbl 0642.60012 |

[28] | Queyranne, M.; Wolsey, LA, Tight MIP formulations for bounded up/down times and interval-dependent start-ups, Math Program, 164, 1-2, 129-155 (2017) · Zbl 1373.90077 |

[29] | Rachunok B, Staid A, Watson JP, Woodruff DL, Yang D (2018) Stochastic unit commitment performance considering Monte Carlo wind power scenarios. In: 2018 IEEE International Conference on Probabilistic Methods Applied to Power Systems (PMAPS), pp. 1-6. IEEE |

[30] | RTS-GMLC (2018) Reliability test system - grid modernization lab consortium. https://github.com/GridMod/RTS-GMLC. [Online; accessed 19-July-2008] |

[31] | Silbernagl M (2016) A polyhedral analysis of start-up process models in unit commitment problems. Ph.D. thesis, Technische Universität München |

[32] | Singh, B.; Watson, J., Approximating two-stage chance-constrained programs with classical probability bounds, Optim Lett, 13, 1403-1416 (2019) · Zbl 1431.90103 |

[33] | Singh, B.; Morton, DP; Santoso, S., An adaptive model with joint chance constraints for a hybrid wind-conventional generator system, Comput Manag Sci, 15, 563-582 (2018) · Zbl 1483.90060 |

[34] | Staid, A.; Watson, JP; Wets, RJB; Woodruff, DL, Generating short-term probabilistic wind power scenarios via nonparametric forecast error density estimators, Wind Energy, 20, 12, 1911-1925 (2017) |

[35] | System Operations Division, PJM (2019) PJM manual 13: Emergency operations revision: 68 effective date: January 1, 2019. https://www.pjm.com/ /media/documents/manuals/m13.ashx. [Online; accessed January 15, 2019] |

[36] | Takriti, S.; Krasenbrink, B.; Wu, LSY, Incorporating fuel constraints and electricity spot prices into the stochastic unit commitment problem, Oper Res, 48, 2, 268-280 (2000) |

[37] | van Ackooij, W.; Lopez, ID; Frangioni, A.; Lacalandra, F.; Tahanan, M., Large-scale unit commitment under uncertainty: an updated literature survey, Ann Oper Res, 271, 1, 11-85 (2018) · Zbl 1411.90214 |

[38] | Wang, B.; Hobbs, BF, A flexible ramping product: Can it help real-time dispatch markets approach the stochastic dispatch ideal?, Electr Power Syst Res, 109, 128-140 (2014) |

[39] | Wang, Q.; Guan, Y.; Wang, J., A chance-constrained two-stage stochastic program for unit commitment with uncertain wind power output, IEEE Trans Power Syst, 27, 1, 206-215 (2012) |

[40] | Watson, JP; Wets, RJ; Woodruff, DL, Scalable heuristics for a class of chance-constrained stochastic programs, INFORMS J Comput, 22, 4, 543-554 (2010) · Zbl 1243.90166 |

[41] | Wu, H.; Shahidehpour, M.; Li, Z.; Tian, W., Chance-constrained day-ahead scheduling in stochastic power system operation, IEEE Trans Power Syst, 29, 4, 1583-1591 (2014) |

[42] | Wu, L.; Shahidehpour, M., Accelerating the benders decomposition for network-constrained unit commitment problems, Energy Syst, 1, 3, 339-376 (2010) |

[43] | Zhao, C.; Wang, J.; Watson, JP; Guan, Y., Multi-stage robust unit commitment considering wind and demand response uncertainties, IEEE Trans Power Syst, 28, 3, 2708-2717 (2013) |

[44] | Zhao, C.; Wang, Q.; Wang, J.; Guan, Y., Expected value and chance constrained stochastic unit commitment ensuring wind power utilization, IEEE Trans Power Syst, 29, 6, 2696-2705 (2014) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.